Efficient evaluation of AGP reduced density matrices

TL;DR

This paper introduces a fast, polynomial-cost algorithm for calculating the norm and reduced density matrices of antisymmetrized geminal power (AGP) wavefunctions, enabling efficient analysis of large quantum systems.

Contribution

The authors develop a quadratic-scaling algorithm for AGP reduced density matrices and provide reconstruction formulas to reduce computational costs further.

Findings

Algorithm scales quadratically per matrix element

Capable of handling systems with thousands of orbitals

Reconstruction formulas reduce higher order RDM computation

Abstract

We propose and implement an algorithm to calculate the norm and reduced density matrices of the antisymmetrized geminal power (AGP) of any rank with polynomial cost. Our method scales quadratically per element of the reduced density matrices. Numerical tests indicate that our method is very fast and capable of treating systems with a few thousand orbitals and hundreds of electrons reliably in double-precision. In addition, we present reconstruction formulae that allows one to decompose higher order reduced density matrices in terms of linear combinations of lower order ones, thereby reducing the computational cost significantly.